they (even if only 10 years older). Along with capital, managers help to create effective employment.
In fact, no one anticipates an immediate drop in the birth rate. In many countries the rate has not yet started to fall; in some it may still be rising. Suppose that in a country that is now increasing at 3 percent, the drop to stationary birth rates takes place in exactly 15 years from now. This means that the population would first increase by about 50 percent, and after that would taper off to a level about two thirds higher. Combining these two increases shows a ratio of 1.50 X 1.67 = 2.50, or an increase by 150 percent to the stationary level. Thus if Mexico were able to arrange a fall in her birth rate to zero increase exactly 15 years from now, she would level off at 125 million (in contrast to a mid-1966 population of 44,145,000).
SMALL CHANGES IN BIRTH AND DEATH RATES AT SPECIFIC AGES
Actually, change will take place more slowly and in small increments. Fertility is not likely to fall uniformly at all ages. Much of the remainder of this paper will discuss the long-term effects of small changes in birth and death rates at specific ages.
Explanation of the Proportion under Age 15 by the Stable Model
That Honduras has a high birth rate and that 51.48 percent of its population is under 15 years of age are intimately related circumstances. Let us see how one follows from the other.
We shall do so by means of what is called the stable model. If a set of age-specific rates of birth and death, the regime of fertility and mortality referred to above, persist over a long enough time in any population, then an age distribution will be reached that is a function of the regime only and in particular is unaffected by the initial age distribution. In the stable distribution the numbers in each group will be increasing at exactly the same rate, say in the ratio X for each 5-year period. Moreover, the births in this imaginary but mathematically determinate population will also be increasing in the same ratio X each 5 years, and so will the deaths. For Honduras X = 1.195; this corresponds to an annual rate r = 0.3564, or 35.64 per 1,000. (Such a rate r is thought of as compounded continuously, a device that considerably simplifies the mathematics and need not detain us here.) The birth rate for the stable condition corresponding to the Honduras regime of 1966 is 10006 = 44.05 and the death rate lOOOc/ = 8.41.
The stable condition resembles the actual one closely in some instances, less closely in others. The interrelations in the stable model are in part transferable to real conditions and help to understand them. In other cases thehey were more numerous, and this means more and better jobs. A further possible advantage of their smaller numbers is a larger ratio of managers to workers if management is provided by those older than